Is it a regular practice to confirm that the application is complete (e.g., all letters of recommendation received)? Or is this considered bothersome? Especially with concerns about emailed letters of rec going to junk mail, what's the common practice for confirming they're received? Or, will a school contact you if they're interested even if they didn't receive all letters?

I did this when I started applying. But then, I'd get some "cold" emails about it and opted to stop. During my search, a few places that extended phone interviews noted that they were waiting for a recommendation letter or other file. Coming from the search committee side, when we had a superb candidate for our most recent search, we were sure to nudge the applicant when we hadn't received all of the application materials.